Cryptology ePrint Archive: Report 2009/025

Short Redactable Signatures Using Random Trees

Ee-Chien Chang and Chee Liang Lim and Jia Xu

Abstract: A redactable signature scheme for a string of objects supports
verification even if multiple substrings are removed from the
original string. It is important that the redacted string and
its signature do not reveal anything about the content of the
removed substrings. Existing schemes completely or partially
leak a piece of information: the lengths of the removed substrings.
Such length information could be crucial for many applications,
especially when the removed substring has low entropy. We
propose a scheme that can hide the length. Our scheme consists
of two components. The first component $\mathcal{H}$, which is a
``collision resistant'' hash, maps a string to an unordered set,
whereby existing schemes on unordered sets can then be applied.
However, a sequence of random numbers has to be explicitly stored
and thus it produces a large signature of size at least $(m
k)$-bits where $m$ is the number of objects and $k$ is the size of a
key sufficiently large for cryptographic operations. The second
component uses RGGM tree, a variant of GGM tree, to
generate the pseudo random numbers from a short seed, expected to be
of size $O(k+ tk\log m)$ where $t$ is the number of removed
substrings. Unlike GGM tree, the structure of the proposed RGGM tree
is random. By an intriguing statistical property of the random tree,
the redacted tree does not reveal the lengths of the substrings
removed. The hash function $\mathcal{H}$ and the RGGM tree can be of
independent interests.